Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints

doi:10.1007/s10483-017-2285-8

摘要/Abstract

摘要： Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem (NCP). An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a constraint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.

关键词: cylindrical shell, general solution, partial differential equation, nonholonomic constraint, nonlinear complementarity problem (NCP), Coulomb dry friction, non-smooth dynamics, two-dimensional friction

Abstract: Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem (NCP). An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a constraint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.

Key words: cylindrical shell, general solution, partial differential equation, Coulomb dry friction, nonlinear complementarity problem (NCP), two-dimensional friction, non-smooth dynamics, nonholonomic constraint

中图分类号:

Ziyao XU, Qi WANG, Qingyun WANG. Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(12): 1733-1752.

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